By the title "DE", is this a differential equation? Does your equation mean y''''+4y=0?

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- Jun 25th 2006, 11:35 AM #1

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- Jun 25th 2006, 02:09 PM #2

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- Jun 25th 2006, 05:38 PM #3

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- Jun 26th 2006, 01:15 AM #4

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- Jun 26th 2006, 03:18 AM #5

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- Jun 26th 2006, 11:36 AM #6

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Originally Posted by**Bert**

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Method 1) (Informal but it works!)

Thus, (square root),

If

Take square roots,

But, Thus,

There are hence 4 possibilities (based on plus minus signs).

Finally if,

then by the same argument you get the same solutions, as before.

- Jun 26th 2006, 11:48 AM #7

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Method 2) (The is the elegant way. [My method if you are curious was to guess and play around with the roots cuz I was too lazy to work it out])

You have,

Express this in polar form,

Now apply, de Moivre's theorem

And the roots are,

one for each value of . And

You get your solutions.

- Jun 26th 2006, 01:54 PM #8

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